Control-oriented model for the dynamic response of a damped cable. (3rd March 2019) - Javanbakht, Majd; Cheng, Shaohong; Ghrib, Faouzi
Abstract: Designing effective control schemes to mitigate the violent vibrations of a stay cable subjected to dynamic loads requires an efficient and accurate computational model for the cable response. In this study, a control-oriented numerical model for evaluating the dynamic response of a stay cable equipped with a damper/actuator is proposed based on the mode superposition method (MSM) with enhanced shape functions. This enhancement accounts for the effect of the truncated higher modes by introducing a static correction term, which is the static displacement of a cable subjected to a point load at the damper location. The exact form is derived analytically and included as a shape function term. Moreover, in the case of a fixed-fixed cable, the outer ends of the sinusoidal shape functions were replaced by polynomials to adapt to the boundary condition. The accuracy and computational efficiency of the proposed model is evaluated through numerical examples and compared to other existing approaches for both passive and semi-active/active control. Results show that the number of modes required to satisfy the convergence criterion would substantially decrease when the static correction term is included. Also, the convergence rate and the numerical accuracy of the proposed model are superior to other methods, which makes it an ideal tool for control design applications. Highlights: Proposed a control-oriented model for the dynamic behavior of a damped cable. Derived enhanced shape functions to significantly improve computational efficiency. Parabolic self-weight profile assumption is acceptable for cable analysis and design. Recommend to design dampers by assuming a fixed-fixed cable boundary condition. The proposed model is more accurate and efficient compared to other methods.